Factorize

With this activity, you can visually explore the concept of factors by
creating rectangular arrays. The length and width of the array are
factors of your number.

This interactive is optimized for your desktop and tablet.

Activity

Instructions

Options

Automatic Number: Numbers will be randomly selected for you.

Use Your Own Number: Select a number between 2 and 50 by typing it into the box.

How to Use

Enter factorizations in the white boxes to the right in the form:

(number)×(number)
(Use either the letter x or an asterisk (*) for the multiplication symbol.)

Need help? Use the grid to help you find the factors. Click and drag to draw a
rectangle. As you draw, the area of your rectangle will be displayed.
Release the mouse button to check your answer. If the area is equal to
your number, the rectangle will stay. If the area is not equal to your
number, it will disappear. The length and width of the rectangle are
factors of your number.

When you've entered your factorization, click the Checkbox
to check your answer. If it is incorrect, the entry will be deleted. If
it is correct, the corresponding rectangle will be drawn on the grid
(if it's not already there).

The number of white boxes corresponds to the number of
factorization for your number. Try to find them all. The rectangles and
factorizations are color coded to help you. The color of the rectangle
matches the highlight color of the factorization box.

Click New Number or enter a new number into the Use Your Own Number box to find the factorizations for a different number.

Exploration

Follow the instructions to find factorizations for several numbers. As you work, see if you can answer these questions:

Why do you think the length and width of the rectangles represent the factors of your numbers?

Which number has the most factorizations? Which has the fewest? Why do you think this is?

What kinds of numbers have only one factorization? What do the rectangles for these factorizations have in common?

If you double a number, what happens to the number of
factorizations? Do you notice a pattern in the factorizations of your
original number and the doubled number?